Concepts Of Physics MCQ Edition [Volume 1]PhysicsFriction
Determine the acceleration of the block of mass M in the arrangement depicted in the figure. The coefficient of friction between the two blocks is ₁ , while the coefficient of friction between the larger block and the ground is ₂ .
Options
- A[2m - ₂(M-m)]g M + m[5 + 2( ₁ - ₂)]
- B[2m - ₂(M+m)]g M + m[5 + 2( ₁ - ₂)]
- C[m - ₂(M+m)]g M + m[5 + 2( ₁ - ₂)]
- D[2m - ₂(M+m)]g M + m[5 + 2( ₁ + ₂)]
Correct answer
B. [2m - ₂(M+m)]g M + m[5 + 2( ₁ - ₂)]
Step-by-step solution
Let a be the acceleration of block M towards the right. Let x be the distance of block M from the wall and y be the distance of block m below the pulley on M . The total length of the string is L = 2x + y + constant . Differentiating twice with respect to time, we get 0 = -2a + a_ y, rel , which implies the downward acceleration of m relative to M is a_ y, rel = 2a . The absolute horizontal acceleration of m is a (towards the right), and its absolute vertical acceleration is 2a (downwards). For block m in the horiz